Application of Control Theory Markov Systems to Minimize the Number of Transmissions in a Multi-hop Network

The classical Robust Control Theory applied to network environments does not consider usual network effects like packet losses in the communication between sensors and actuators. In order to design optimal controllers that consider such conditions, one must rely on the class of models dubbed Markovian Jump Linear System (MJLS). In this paper, we study the H-infinity norm degradation in the presence of a limitation on the allowed number of retransmissions in a multi-hop semi-reliable network. Specifically on this study, we implemented the Hop by Hop transport model and also limited the maximum number of retransmissions per packet. For a particular case, it was possible to design a filter with a global number of transmitted packets of only 17.93% of the packets that would be necessary in full reliable communication, yet guaranteeing the estimated error stability.